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Rigidity of mass-preserving 1-Lipschitz maps from integral current spaces into Euclidean space

Connections Workshop: New Frontiers in Curvature & Special Geometric Structures and Analysis August 21, 2024 - August 23, 2024

August 22, 2024 (11:00 AM PDT - 12:00 PM PDT)
Speaker(s): Raquel Perales (Cimat)
Location: SLMath: Eisenbud Auditorium, Online/Virtual
Primary Mathematics Subject Classification No Primary AMS MSC
Secondary Mathematics Subject Classification No Secondary AMS MSC
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Rigidity of mass-preserving 1-Lipschitz maps from integral current spaces into Euclidean space

Abstract

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We will prove that given an n-dimensional integral current space and a 1-Lipschitz map, from this space onto the n-dimensional Euclidean ball, that preserves the mass of the current and is injective on the boundary, then the map has to be an isometry. We deduce as a consequence the stability of the positive mass theorem for graphical manifolds as originally formulated by Huang--Lee--Sormani. (Joint work with G. Del Nin).

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Rigidity of mass-preserving 1-Lipschitz maps from integral current spaces into Euclidean space

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